ML without tears

Tag: machine-learning

  • Maximum Mean Discrepancy (MMD): The Infinite Moment Matchmaker

    Consider the problem of measuring the discrepancy between the distributions of two sets of samples and . Amongst various options (KL divergence, Wasserstein distance, etc.), the Maximum Mean Discrepancy (MMD) is a beautifully elegant one, gaining popularity in recent years in the machine learning community. In this post, instead of defining upfront the MMD in…

  • Understanding PPO from first principles

    Proximal Policy Optimization (PPO) algorithm is arguably the default choice in modern reinforcement learning (RL) libraries. In this post we understand how to derive PPO from first principles. First, we brush up our memory on the underlying Markov Decision Process (MDP) model. 1. Preliminaries on Markov Decision Process (MDP) In an MDP, an agent (say,…

  • Lagrangian multipliers, normal cones and KKT optimality conditions

    We consider constrained optimization problems of the kind: where the feasibility region is a polytope, i.e., is the set of such that: where are real matrices of size and , respectively, and are column vectors. Equivalently, we can rewrite (1) as: where are the -th row of and , respectively, and denotes the scalar product. In this post we…

  • Get real! Solving a complex-value linear system using real arithmetic

    Consider a linear system of complex-valued equations of the kind , where are complex square and rectangular matrices, respectively, and is the unknown complex matrix. To compute , a natural option is to use any algorithm available in the literature initially conceived for real systems, such as Gauss elimination, LU/Cholesky decomposition, and translate its operations to complex arithmetic. However, there may…